Theoretical Study on the Anomalous Electronic States of Mixed-Valent Vanadium Oxides with Trellis-Lattice Structure

过渡金属氧化物是典型的具有强电子相关性的材料，包括一类具有混合价状态的化合物。这些体系的荷电自由度经常表现出反常的行为，因此引起了实验和理论的广泛关注。在我们的项目中，我们特别关注了具有网格结构的α‘-NaV_2O_5，β-Ag_&lt；0.33&gt；V_2O_5(A=Li，Na，Ag，Ca，Sr)和β’-CuxV_2O_5(x=0.65)等钒氧化物材料，以及一种新的钒酸盐材料BixV_8gO_&lt；16&gt；研究了它们的电荷有序化(CO)、金属绝缘体转变(MIT)与CO的微观起源、压力诱导超导电性以及MIT与CO和轨道有序(OO)的微观起源。在下面，我们列出了我们在本项目中取得的代表性成果。1.研究了格子-格子t-J模型在1/4填充时的电子态，并从其光学电导计算…对α‘-NaV_2O_5的进一步计算表明，在转变温度以上存在反常电荷涨落。此外，为了阐明存在大电荷涨落时自旋系统的磁响应，我们开发了一个新的量子蒙特卡罗方法的计算机程序。2.对于β相钒青铜，我们研究了MIT伴随CO以及相关的反常电子性质。特别是，我们提出了该体系中的MIT是由自掺杂引起的机理。此外，我们还提出了实现这一机制的最简单的模型“四分之一填充时的中心Hubbard梯形模型”，并用平均场计算和密度矩阵重整化群方法仔细研究了该模型的电子态。3.对于相关材料，我们取了一些有机导体和PrBa2Cu4O8中的CuO双链，阐明了CO的来源和反常的光谱。对于最近被认为是MIT的CO和OO体系的新材料BixV8O&lt；16&gt；，我们建立了一个基本模型，并提出了它可能的CO和OO空间模式。较少

Transition-metal oxides, materials typical of strong electron correlation, include a class of compounds with mixed valent state. The systems often show anomalous behaviors in their charge degrees of freedom and thus have attracted much attention from both experimental and theoretical viewpoints. In our project, we have paid particular attention in vanadium-oxide materials such as α'-NaV_2O_5 with trellis-lattice structure, β-Ag_<0.33>V_2O_5 (A=Li, Na, Ag, Ca, Sr) and β'-Cu_xV_2O_5 (x=0.65) with two-dimensional structure, and a new vanadate material Bi_xV_8gO_<16> with a one-dimensional framework and have studied microscopic origin of their charge ordering (CO), metal-insulator transition (MIT) with CO, pressure-induced superconductivity, and MIT with both CO and orbital ordering (OO). In the following, we list up our representative results obtained in our project. 1. We studied electronic states of the trellis-lattice t-J model at quarter-filling, and from its optical conductivity calc … More ulation for α'-NaV_2O_5, we showed the presence of anomalous charge fluctuation above the transition temperature. Furthermore, to clarify magnetic response of the spin system in the presence of large charge fluctuation, we developed a new computer code of the Quantum Monte Carlo method. 2. For β-phase vanadate bronzes, we made studies of MIT accompanied by CO and related anomalous electronic properties. In particular, we propose a mechanism that the MIT in this system be caused by the self-doping. Moreover, we present the simplest model "Acentric Hubbard ladder model at quarter filling", in which this mechanism is realized, and we carefully examined the electronic state of the model by using mean-field calculation and density-matrix renormalization group method. 3. As for related materials, we took some organic conductors and CuO double chains in PrBa_2Cu_4O_8, and clarified the origin of CO and anomalous optical spectra. Also for a new material Bi_xV_8O_<16>, which is recently recognized as a system of MIT with CO and OO, we constructed a basic model and proposed its possible CO and OO spatial pattern. Less